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Instantaneous deflection of the semi-rigid beam at mid-span, 5inst i2 (5 ■ Fb.d.SLS ■ ib ^SR.m.d.SLS^ , 1-2 ■ Vd.SLS ■ ib Oinst = —-r- ■ ----^- +

Instantaneous deflection of the rigid beam at mid-span, 51inst i2 (5 ■ Fb.d.SLS ■ i2 F,.d.SLS ■ i2 V 1.2 ■ Vd.SLS ■ ib

01 inst = 2.15 mm i.e. fully rigid beam deflection is only about 50% of the semi-rigid value mean

Example 12.8.3 A timber roof structure is formed from 300 mm deep by 75 mm wide timber beams supported by columns as shown in Figure E12.8.3. Each beam is connected at its ends to the adjacent beams by steel brackets, such that the beam can be considered to form a continuous semi-rigid structure. At each end of the roof structure the steel bracket is fixed to a rigid support on adjacent structures.

The connection detail between adjacent beams at the ridge level is shown in Figure E12.8.3. It is an 8-mm-thick steel plate fitted within a notch in the beams and the connection is formed using 8 No 12-mm-diameter mild steel bolts and the bolt spacings comply with the requirements of Table 12.3. A similar bracket is used to connect adjacent beams at the eaves level and the rigidity factor for that connection is only 40% of the rigidity factor of the beam connection at the ridge. At the eaves level, the steel brackets are connected across the structure by steel ties and these can be considered to be axially rigid. The beams are strength class C24 to BS EN 338:2003 and the effective span of each beam along the direction of its longitudinal axis can be taken to be 3700 mm. Each beam is restrained from lateral buckling and lateral torsional movement at the ends and at the mid span positions. The design loading acting vertically on plan on each beam, which includes for the effect of the self-weight of the beam, is 8.5 kN/m, and arises from a combination of permanent and medium-term variable loading. The largest stress in relation to strength will be due to the variable loading and in accordance with the requirements of EC5, 2.3.2.2(2); f2 will be 0. The structure functions under service class 2 conditions.

Taking semi-rigid behaviour into account, check that the connection at the ridge will comply with the strength requirements of EC5 and that the bending, axial and shear strength of the beams will be acceptable.

1. Geometric properties

Tensile stress area of a bolt, Ab.t Ab.t = 84.3 mm2

Number of bolts per shear plane, «bolt «bolt = 8 Bolt distances from the centroid of the group - relative to the grain:

Horizontal distance along grain to the x = 100 mm extreme bolt a, x

8.5 kN/m design loading llllllllllllllllllllllllllllllll

(a) Roof structure elevation

End A

8 No 12-mm-diameter 100 bolts per connection 100

End A

8 No 12-mm-diameter 100 bolts per connection 100

Connection detail is the same as shown across

75 mm by 300 mm C24 timber beam

8-mm-thick steel plate

Connection detail is the same as shown across

75 mm by 300 mm C24 timber beam

8-mm-thick steel plate

3700 mm to the centre line of the connection at End B of the beam

8-mm-thick steel plate

8-mm-thick steel plate

12-mm-diameter bolt

75 mm by 300 mm C24 timber beams

All dimensions are in mm

Vertical distance perpendicular to the grain to the extreme bolt a, y Thickness of the steel plate in the timber member, tsteel Thickness of the timber member, t2

Thickness of the side timbers at the joint, ts

Depth of the timber member, h Moment of inertia of the beam, Ib

Section modulus of the beam, Wb

Clear span of each bent, t

Effective length for lateral buckling about the y-y axis, Le,y (based on the content of Table 5.2, adopt a factor of 0.9tb)

Effective length for lateral buckling about the z-z axis, Le,z (based on the content of Table 5.2, adopt a factor of 0.5tb)

Cross-sectional area, A

Second moment of area about the y-y axes, Iy

Section modulus about the y-y axes, Wy y = 95 mm isteei = 8 mm t2 = 75 mm i2 tsteei ts

0 0

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